My understanding is that most everything in FLA's gets recycled. Are they able to recycle Li-ions?
Most everything in FLAs CAN be recycled. The big nasty - lead - has some value, too.
Whether they ARE recycled is another can of worms. (My wife, part American Indian, claims that many/most of them end up in big piles on certain reservations where the tribe has permitted them to be dumped, rather than actually being recycled and the toxic materials reused.)
Lithiums are made mostly of cheaper stuff, which is (allegedly) not nearly so toxic as FLAs. So on one hand they may be less of a hazard if dumped, but on the other there's less incentive to actually salvage and reuse their contents, rather than dumping them somewhere and making new ones from scratch.